If selection acts on synonymous sites, by comparing a real mouse mRNA to simulants differing only at synonymous sites, we should find that, on average, the real transcript is more stable. For each gene we generated 1,000 random mRNAs identical in all regards to the real sequence, but with the bases at 4-fold degenerate (synonymous) sites in the coding sequence (CDS) randomly shuffled between the 4-fold degenerate positions. For each mRNA we determined Z(ΔG), the number of standard deviations the real mRNA is away from the mean stability of the simulants. Z(ΔG) is thus a measure of 'relative stability', the stability of a given mRNA relative to what one would expect by chance alone. Relative stability can also be considered as a measure of the strength of selection for stability, with a negative Z-score implying higher than expected stability. As Table 1 shows, real mRNAs are, on average, highly significantly more stable than 'Sh.4-fold' simulants (Figure 1; Additional data files 2, 3). Note, however, that on an individual basis, the effect (if any) is weak, with only 26 (37%) of genes having significantly high relative stability at the 5% level (Additional data file 4). Moreover, were we to apply Bonferonni correction for multiple testing on the by-gene P-values, no more than four genes would be significant at the 5% level. Inspection of the genes in our dataset (Additional data files 5, 6) did not reveal an obvious pattern that relates relative stability to their function.

In organisms from large effective populations, bias in codon usage is usually attributed to translational selection, favoring efficient (fast and/or accurate) protein synthesis as a consequence of skews in iso-acceptor tRNA abundance (reviewed in 75859). Whether this occurs in mammals, however, remains a contentious issue. While some have suggested that preferred sets of codons do exist to match the most abundant tRNAs 60, others maintain that codon usage does not reflect tRNAs skews 761 and that translational selection does not occur 62. To be cautious, however, we also employed a protocol ('Sh.codon') that preserves the relative frequency of codons within a given set by shuffling codons within synonymous sets. This protocol gave very similar results to the previous ('Sh.4-fold') randomization (Table 1; Additional data files 2, 3).

While the above results suggest that the identity of the nucleotide at any given synonymous site is non-random, this need not reflect maintenance of mRNA stability. Selection could instead be acting on a thermodynamic property of DNA, such as bendability 63. As more G:C pairings make helices more bendable and gene-dense regions are GC-rich (for example, see 64), the putative selection on GC content we observe at the mRNA level might actually function to provide the transcriptional machinery with easier access to the most gene-dense regions of DNA. To address this issue, we asked about the strand-specific preference for cytosine at 4-fold degenerate sites observed in rodent exons 15.

Cytosine preference is indicated by two related features: a higher C content at 4-fold sites than in flanking introns (not observed for guanine) and an excess of C over G at 4-fold degenerate sites 15. Correspondingly, we found C4 > G4 in 87% of our mouse genes and a mean skew in GC4 (G - C/G + C) of -0.1506 (P = 1e-11 for expected mean (μ) < 0 by one-sample t-test on GC4 skew). Importantly, the skew towards C is specific to exons and, therefore, cannot be accounted for by effects at the DNA level (for example, mutational biases such as transcription-coupled repair, or selection on transcription). Note also that the sign of the skew is the opposite of that derived from transcription-coupled repair, which yields a G excess 6566. Significantly, introducing synonymous changes that increase C|G dinucleotide content (where | is the codon boundary) extends mRNA half-life in vitro while increasing A|U enhances degradation 36. If selection is acting on mRNA stability, then this could be explained by a high C content at third sites increasing the number of potential G:C base-pairs, which are stronger than A:U interactions (triple and double hydrogen bonds, respectively). Consistent with this, we find that genes with the highest relative stability also have a greater excess of C over G (Spearman rank correlation coefficient (ρ) = 0.27, P = 0.0225 for GC4 skew versus Z(ΔG^Sh.4-fold); Additional data file 7).

To further examine the possibility that the C preference is explained by selection on RNA structure, we also asked whether replacing C residues with G decreases stability. We found that real mRNAs are more stable than modified transcripts in which, at 4-fold sites, we swapped all Cs for Gs and vice versa (Table 1; Additional data files 2, 3). 'Swap G4C4' mRNAs, however, possess a higher percentage of base-pairs than real transcripts (62.11 ± 0.33% and 60.96 ± 0.28% in CDS, respectively, P = 0.0003 by paired t-test; 60.84 ± 0.26% and 61.61 ± 0.26% in mRNA, P = 0.0007). That 'Swap G4C4' mRNAs have more base-pairs but lower stability can be explained by the existence of G:U base-pairs within stems, as G:Us are weaker than Watson-Crick interactions (A:U and G:C). An increased G content increases the amount of G:U pairs (real 10.50 ± 0.26% and 'Swap G4C4' 11.64 ± 0.21% in mRNA, P = 3e-07) and thus the proportion of base-paired mRNA, but their stems are less stable (there is no difference in the proportion of A:U pairs: real 36.60 ± 0.70%, 'Swap G4C4' 36.39 ± 0.71%, P = 0.2449). These results further underline the importance of nucleotide content for mRNA rather than DNA stability, not least because the location of bases that can potentially form Watson-Crick base-pairs in DNA is preserved in the modified transcripts.

The results above suggest that, given the nucleotide content at non-synonymous sites, C enrichment at synonymous sites is adaptive in regards to mRNA stability. Is there something about non-synonymous sites that causes C in particular to be enriched at synonymous sites? Fitch 17 proposed that, if genetic code degeneracy is exploited to optimize base-pairing in mRNA, third sites within codons (usually synonymous) should be preferentially paired with first and second sites (few and no synonymous sites, respectively). This would also provide a buffer for mRNA structure against non-synonymous substitutions via compensatory changes. Cytosine preference at third sites might, therefore, be driven by selection on amino acid content and mRNA stability 19.

In stems, we expect that, to permit base-pairing, a high G content at first and second sites should be matched by a high C content at third sites (and vice versa), that is, selection on non-synonymous sites would, at least in part, dictate nucleotide content at synonymous sites. At base-paired sites in mRNAs, there is a strong negative correlation in GC skew between first/second sites and third sites (for example, Pearson correlation coefficient (R) = -0.65, P = 1e-09 for GC12 skew versus GC3 skew) that is not observed at unpaired sites (R = 0.70, P = 1e-11; Additional data file 7; note that a positive correlation is expected from isochore structure 67).

Given the potential inaccuracies of minimum free energy prediction methods (see Materials and methods), we also asked whether the above relationship is robust to the exclusion of sites at which one is less confident that base-pairing occurs (either with a particular site in the optimal structure or with any other site). GC skew is then only calculated for those sites where the probability of pairing is greater than some minimum threshold. We found that the significant negative correlation in GC skew between first/second and third sites is strikingly insensitive to different threshold values (Additional data file 8).

Jia et al. 68 recently observed that α-helices and β-sheets of protein secondary structures are preferentially 'coded' by mRNA stems. Using data on the amino acid preferences for protein conformations 69, we found G to be more abundant than C at first and second sites in both α-helices and β-sheets (GC12 skews of 0.001 and 0.0420, respectively). Similarly, there is a bias towards G in these regions within the proteins from our dataset (α-helix GC12 skew of 0.0608 ± 0.0143, P = 8e-05 for μ = 0 by one-sample t-test; β-sheet skew of 0.0879 ± 0.0312, P = 0.0102). The C preference at third sites may, therefore, reflect selection to maintain stable stems in these regions enriched for G at largely non-synonymous sites.

While randomization protocols that shuffle or swap nucleotides provide insights into how putative selection for mRNA stability and nucleotide content interact, these processes do not occur in nature. The most direct evidence that we can consider is to examine the locations of observed synonymous mutations. Reallocating point mutations is a more realistic form of analysis as it mimics the process of selection following mutation (nucleotide substitutions that are not the result of single point mutations are very rare in mammals, for example, see 70717273). This minimizes potential biases. For example, randomization protocols that shuffle nucleotides or codons (for example, see 42) might be problematic 74 as they generate a large number of variants in which there will be a profound effect on dinucleotide relative abundances 757677. Simulating the process of evolution, however, only introduces 7 to 8 synonymous changes per 100 sites, hence only about 1 to 2 per 100 nucleotides in the coding sequence. This will have negligible impact on dinucleotide distribution.

Parenthetically, as recent evidence suggests that dinucleotide content in rodent exons is the result of selection 15 and not of biased mutation and/or repair 5675, the desirability of controlling for dinucleotide distribution is highly questionable. Put differently, if a real mRNA is on average more stable than expected when compared to simulants in which the observed point substitutions have been reallocated, biased dinucleotide distribution is more likely to be a consequence of selection for favorable base-stacking interactions rather than mutational/repair biases.

If certain mutations really were under selection because they diminished mRNA stability, relocating those substitutions actually seen to random locations ('Re-sub.') should lower stability. We used parsimony to determine the substitutions that have arisen in the mouse lineage, inferring the CDS of the rat-mouse common ancestor using hamster as the outgroup to maximize reliability and the number of informative sites (Additional data file 9). We reverted all synonymous changes back to the ancestral state and then simulated mutation by randomly reallocating substitutions at synonymous sites, maintaining the number of observed changes and the encoded protein.

Note that the application of parsimony, while a common practice in the mouse-rat comparison (for example, see 7879), can sometimes provide biased ancestral state reconstructions (for example, see 80). We therefore also reconstructed rat-mouse common ancestor sequences using a maximum likelihood approach. At only 3 of 86,334 reconstructed sites did the parsimony and maximum likelihood methods disagree (excluding sites differing in all three species, see Materials and methods). All three discrepancies occurred in the same gene (Gadd45a). Exclusion of this one gene makes no difference to our results (Additional data file 2).

As nucleotide content is influenced by genomic location (isochores; for example, see 67), the re-introduced nucleotides were selected at random, but in proportion to base composition at third sites in the appropriate mouse gene. This also further minimizes the negligible effect on dinucleotide distributions. From this randomization ('Re-sub.N3') we again find that real mRNAs are, on average, more stable than expected by chance (Table 1; Additional data files 2, 3). Ignoring the effect of isochores and changing the profile of permitted substitutions does not qualitatively alter this result. For example, allowing all mutations to occur with equal likelihood ('Re-sub.K') also shows that the locations of observed substitutions have had minimal impact on stability (Table 1; Additional data files 2, 3). Simulants and real transcripts possess a similar amount of base-pairs (P > 0.15 by one-sample t-tests on Z(%base-pairs), μ = 0; Table 1).

While the above results indicate that the location at which certain synonymous mutations are observed is in part determined by constraints on mRNA stability, could the above results be artifacts of an inaccurate methodology? We have attempted to minimize such problems by considering those sequences in which a priori we expect the method to be more accurate and by considering only those sites that have a high probability of being base-paired. We can, however, consider additional tests. If selection for mRNA stability occurs, we also expect that substitution rates should be related to predicted stem-loop structure and that genes known to be under strong purifying selection should possess mRNAs with high relative stability. We examine these two predictions in turn.

Testing the first prediction, that evolutionary rates should be linked to mRNA secondary structure, is not straightforward, even if structure prediction were perfect. Although one expects that the majority of compensatory changes will occur to restore substructures, the thermodynamic hypothesis posits that some will also act to restore the overall stability of the molecule. Even if a precise secondary structure were conserved, the difficulty lies in the fact that a given substitution can only be assigned to having occurred within a stem or loop before or after it potentially affects base-pairing, for example, a transversion at a base-paired site in the ancestral mRNA will create a bulge/loop. Consequently, the only substitutions that can be observed within the same (conserved) structure of the descendant sequence are those that arise within loops with little stem-forming potential or within stems in which a compensatory substitution has restored complementary base-pairing. With this caveat in mind, we examined observed substitutions with respect to the predicted secondary structure in mouse.

We first asked whether substitution rates correlate with the percentage of sequence involved in base-pairing interactions. We found that both the number of synonymous substitutions per synonymous site (Ks) and the non-synonymous substitution rate (Ka) for the whole CDS are higher in genes with more base-pairs (K_a ρ = 0.31, P = 0.0091, N = 70; K_s ρ = 0.31, P = 0.0101, N = 69), although the result for non-synonymous mutations is sensitive to restricting analysis to the subset of small mRNAs (Additional data file 10). These effects seem to be a consequence of substitutional processes within stems. While there is a positive correlation between %base-pairs and rates within putative stems (K_a ρ = 0.31, P = 0.0090, N = 69; K_s ρ = 0.37, P = 0.0020, N = 68), no such relationship exists in loops (K_a ρ = -0.03, P = 0.7941, N = 69; K_s ρ = -0.03, P = 0.8264, N = 69; Additional data file 10).

Note that these latter correlations do not mean that stems evolve faster per se (one would predict the opposite), only that they may evolve faster when a lot of the sequence is base-paired. Indeed, consistent with stems being under purifying selection to maintain secondary structure, while non-synonymous rates are the same between codons in putative stems and those in loops (P = 0.6233, N = 69 by paired t-test, stem = 0.0110 ± 0.0018, loop = 0.0095 ± 0.0012), synonymous sites in loops evolve 37% faster than those in stems (P = 0.0045, N = 68, stem = 0.0833 ± 0.0071, loop = 0.0608 ± 0.0034; Additional data file 10).

Why might a high proportion of base-pairing be associated with rapid substitution rates within stems? One possibility is that an abundance of base-pairs ensures that no single mutation can grossly destabilize an mRNA. While one might then predict a negative correlation between %base-pairs and Z(ΔG) (that is, changes to mRNAs with little secondary structure will have a large impact on stability), this may not be observed because when substitutions are randomly reallocated the majority will not fall within stems. Alternatively, the relationship between %base-pairs and substitution rates within stems may indicate a high rate of compensatory changes restoring stem structures. Consider a mutation that arises within a stem that destabilizes the mRNA secondary structure. If selection maintains transcript stability, the substitution will only be tolerated if it is adaptive at the protein level or has such a negligible impact on stability as to be effectively neutral. In the latter case, further changes could accumulate that in combination might significantly alter structure. Under both scenarios, subsequent compensatory mutations restoring stability would thus be under positive selection. The effect of one mutation arising within a stem that has the knock-on effect of increasing substitution rates within stems would be most pronounced in genes with a high proportion of base-pairing. Consequently, compensations would be most favored when there is high pressure to maintain stability. Indeed, we find that in those genes under the strongest selective pressure for high stability, putative stems are fast-evolving (ρ = -0.37, P = 0.0020 for Z(ΔG^Re-sub.N3) versus K_s, N = 68).

To test the second prediction, it is necessary to define a priori a set of genes likely to be under stronger purifying selection. Prior evidence indicates that genes expressed in most tissues, housekeeping genes, may be good candidates for two reasons. First, housekeeping proteins evolve slower than tissue-specific ones 73818283. Second, experimental assays of half-life have demonstrated that mRNAs of housekeeping genes degrade relatively slowly 5354.

Here we identify housekeeping genes by calculating the breadth of expression, the proportion of tissues in which a given gene is expressed. We call a gene 'expressed' in a particular tissue if the average hybridization intensity on microarrays ('average difference' (AD)) for the transcript is greater than 100 or 200 (approximately 2 or 4 copies per cell, respectively, 84). Housekeeping genes are those expressed in a large proportion of tissues. As described previously (for example, see 73), we found that protein evolution is slowest in housekeeping genes (%tissues versus K_a: ρ = -0.39, P = 0.0008 for AD > 200; ρ = -0.32, P = 0.0065 for AD > 100).

Significantly, consistent with the prediction, we found that genes subject to strong purifying selection (housekeeping genes) also have the highest relative stability, with the inferred intensity of selection on mRNA stability being correlated with breadth of expression in the expected direction (ρ = -0.25, P = 0.0335 for %tissues versus Z(ΔG^Re-sub.N3) at AD > 200). Using a less conservative cut-off to define a gene as expressed (AD > 100) increases the strength and significance of the correlation (ρ = -0.29, P = 0.0159). The relationship becomes more pronounced after controlling for sequence length (partial ρ = -0.25, P = 0.0179 for AD > 200; partial ρ = -0.30, P = 0.0069 for AD > 100; significance determined by 10,000 randomizations). Expression breadth is not associated with the proportion of the sequence that is base-paired (ρ = -0.01, P > 0.9 for %tissues versus %base-pairs in CDS), nor does the amount of base-pairing predict relative stability (R = -0.14, P = 0.2630 for %base-pairs versus Z(ΔG^Re-sub.N3)). As suggested from the 'Swap G4C4' modification protocol, this supports the importance of overall stability over the amount of secondary structure.

One might suppose that in silico simulations could explain variation in decay rates between genes. Z(ΔG) is not a measure of absolute stability, however, but rather of stability relative to what might have been observed given the underlying parameters of a gene, such as length and coding capacity. Only if all such parameters were equal between genes would one expect relative stability to predict decay rate. However, all else is not equal; for example, we find that Z(ΔG) and nucleotide content covary. Therefore, looking for a correlation between Z(ΔG) and half-life 56 is a weak test because an absence of a relationship would not be strong evidence against the hypothesis unless other variables could be controlled. Indeed, results are ambiguous. Mammalian housekeeping genes have longer half-lives 5354 and we find that they also have high relative stability. In contrast, Katz and Burge 56 found no correlation between decay rate and local Z(ΔG) in yeast. The interpretation of the yeast result is made even less clear due to uncertainty over when mRNAs should be folded globally. The issue might be easier to resolve once high-quality non-human sequence from primates becomes available, as one could then compare available large-scale surveys of human mRNA decay rates (for example, see 54) with relative stability. As hominid N_e is around an order of magnitude lower than in murids 88, however, it is also conceivable that selection may not be strong enough to act on mRNA stability.

On the other hand, simulations should predict relative decay rates of mutant versions of a given gene. In at least one case, the dopamine receptor D2 gene, it has been demonstrated that only single nucleotide polymorphisms that induce a conspicuous change in structure predicted in silico affect mRNA half-life in vitro 35. A much larger sample set is required to determine whether this is more generally true. We predict that, for those genes with the highest relative stability, the real mRNA should have a longer half-life than the majority of mutants in which one has randomly reallocated synonymous mutations.

That selection maintains mRNA stability contradicts the accepted wisdom that synonymous mutations evolve neutrally 12, not only because changes do not alter protein sequence, but also because mammalian effective population sizes (N_e) are thought to be too small to permit selection on mutations of small effect on fitness 6. Moreover, nucleotide content at silent sites in mammals is best predicted by genomic location (isochores; for example, see 67). Our observations, however, nonetheless tally with recent evidence that selection acts on synonymous mutations 10111213141516.

Selection favoring accurate or fast protein synthesis, the classically cited functional role for biased usage of synonymous codons, is not well supported in mammals 76162. Translational selection predicts that highly expressed genes should exhibit the greatest bias in codon usage 7, but the effect is only weak 136089 and a bias is also observed in lowly expressed genes 89. On the other hand, selection for mRNA stability need not correlate with expression level (indeed, we find no relationship between Z(ΔG) and mean or peak expression level; P > 0.1 in all cases).

When translational selection is known to occur, it can be at odds with selection for mRNA secondary structure (fly, 20) and stability (yeast, 90), leading to a trade-off between the two forces 2090. Given the difficulties involved in detecting codon usage bias in mammals 7 and our results above, we infer that selection on mRNA stability must be strong relative to translational selection (if the latter occurs at all). This has two repercussions. First, selection for mRNA stability could, in principle, weaken any signal of a preferred set of codons for translational efficiency. Second, in terms of detecting selection at synonymous sites in mammals, asking whether a given amino acid always prefers a certain codon is not necessarily asking the right question. Indeed, it is quite possible that there exist no preferred codon within a gene while at the same time synonymous mutations are under selection. More generally, a complex set of trade-offs between different forms of selection and mutational biases may render interpretation of patterns of codon usage very difficult.

The evidence for selection on synonymous mutations also has implications for our understanding of both the mutation rate and the mutational load. The substitution rate at synonymous sites in exons is often used as a measure of the mutation rate 89; however, this assumes neutral evolution of synonymous mutations 12. By providing a parsimonious mechanism by which selection could act on synonymous sites, we can ignore the objection that prior evidence is indirect. Nevertheless, it is presently unclear to what degree synonymous mutations are favored or opposed by selection due to their effects on mRNA stability. Without being able to quantify the latter, as well as the net effect of other biases (for example, splice-associated), it will not be possible to directly estimate the extent to which use of the synonymous substitution rate leads to underestimates of the mutation rate and the mutational load.

We identified gene families from HOVERGEN (Release 44) 9192 with complete CDSs for Mus musculus, Rattus norvegicus and hamster. Orthology was defined as the topology (((mouse, rat), hamster), non-rodent outgroup) within the phylogenetic tree for a given gene, without intervening non-rodent branches between the rodents. Seventy well-described genes matched these criteria and had a <5% size difference between the longest and shortest CDS. Non-redundancy and orthology were supported by syntenic comparisons 93. Unless otherwise stated, N = 70 for all statistical tests.

Accession numbers from HOVERGEN were used to extract mRNAs from the EnsEMBL genome assembly (Build 30) 94. When alternative transcripts existed, we used the rat and hamster sequences to identify the desired exons. The untranslated region (UTR) database (Release 15) 9596 was used for six genes because the UTRs in the EnsEMBL files were unreliably annotated. If present, poly(A) tails were removed as they are coated with binding proteins and so are unlikely to be involved in base-pairing 97.

Each CDS was extracted using GBPARSE 98 and translated. We aligned amino acid sequences as previously described 15 then reconstructed the three-way nucleotide alignment using AA2NUC (available from L.D.H.).

Parsimony and maximum likelihood were used to reconstruct ancestral sequence. At 0.3% of sites in the rodent alignment, the rat-mouse ancestral state could not be determined (for example, a different base was present in each species). In these cases, we used the mouse sequence to be conservative for the number of substitutions that have occurred in the mouse lineage. Ancestral states derived from maximum likelihood were determined using codeml in the PAML package 99100.

There are two main computational approaches to predicting RNA secondary structure. The first is a thermodynamic method, which assumes that a given sequence will fold into the structure with the minimum free energy 101. The second approach compares multiple orthologous sequences to identify patterns of co-evolution between sites that could be indicative of compensatory mutations 102 to maintain complementary base-pairing within stems 103104105106107108.

In the context of our analysis, the choice is highly constrained and comparative methods may not be applicable to the hypothesis we test. Comparative methods require all input sequences to be of high quality and for the alignment to be accurate. Here we are particularly interested in knowing where substitutions have occurred in a given mammalian lineage and, therefore, need sequence from three species, with mouse-rat-hamster being the obvious choice. Currently, however, rat genomic sequence is not of sufficiently high quality and annotation of UTRs is unreliable. UTRs from hamster are largely unavailable.

Although a moot point under the above circumstances, it may also be undesirable to apply a comparative method in the current context, not least because the logic would be circular: the method requires us to assume that selection is strong enough to maintain secondary structure, while at the same time we are testing for selection. More importantly, based on the evolution of non-coding RNAs, comparative methods are geared towards detecting secondary structure that has been conserved despite sequence divergence 49, that is, well-conserved substructures exist which tend to have specific functions (for example, the anti-codon within a tRNA must always be within a loop). For mRNA, however, a more realistic model is that selection favors the stability of the mRNA conformation as a whole 1718. Highly conserved substructures are not expected a priori 109, in part because such conservation may not always be possible, as protein-coding function should outweigh any RNA structure considerations. Essentially, the model assumes that the mRNA will adopt the optimal structure given the available sequence.

Structure and stability were predicted using RNAfold from the Vienna package (Version 1.4) 110111 under default settings (folding at 37°C, tolerating non-Watson-Crick G:U pairs). Thermodynamic parameters were derived experimentally 112. RNAfold implements an algorithm that, for a given RNA, finds the conformation with the minimum free energy by maximizing favorable base-pairing interactions 101.

A second methodological issue concerns whether selection might act on stability at the local or global scale. There are two critical issues when choosing which to assess. First, if opposite ends of a molecule are able to pair with one another, RNAs may adopt a conformation closer to a global optimal structure. In eukaryotes, unlike bacteria (where transcription and translation are simultaneous and co-localized), long-range interactions between opposite ends of mRNA molecules can occur 113114115116. This suggests that global 20 rather than local stability is more important to analysis of mammalian sequence.

Second, one must also ask whether the genes contain introns. Generation of a globally stable structure would require the action of spliceosome-associated helicases (for example, 117118119) to maximize the amount of available sequence. Indeed, it is significant that intronless genes in yeast are less biased for structure than those with introns 56. All genes in our dataset contain introns, further suggesting global stability to be the more relevant measure. Nonetheless, our assumption of global maximum stability, while an appropriate functional hypothesis, may at best only be a good approximation, as in some cases (for example, short transcripts) there may not be enough time for an mRNA to discover the most optimal structure.

While minimum free energy predictions often agree with laboratory-based methods (for example, stem-loops are avoided at the AUG initiation codon, 120121122123), they are less reliable for long sequences (for example, 112). The mean length of transcripts in our dataset is 2,101.41 ± 139.84 nucleotides (nt). Consequently, where relevant, we endeavored to control for length effects. In most cases, we carried out the same analyses for mRNAs shorter than 2,000 nt (N = 36, mean mRNA length of 1219.38 ± 77.32 nt), this being the cut-off defining two halves of the dataset. Through Mantell simulations, we found that, when testing for selection on stability, in no instance is the P-value for the smaller dataset both not significant and higher than that expected if one were to randomly sample half the dataset, where the full data set analysis suggested significance (Additional data file 3). Consequently we conclude that the results are not obviously biased by the inclusion of long sequence.

The attributes of mouse gene products were obtained from the Gene Ontology database (June 2004) 124.

Amino acid sequence was designated as occurring in α-helix, β-sheet (strand) and coil regions using PSIPRED (Version 2.3) 125126 under default parameters (masking low complexity regions).

The number of non-synonymous substitutions per non-synonymous site (K_a) and the synonymous (K_s) distance were estimated with the Li method 127 using the Kimura 2-parameter model. We excluded one fast-evolving gene (K_a = 0.5; K_s = 0.17) in our analyses of evolutionary rates, although inclusion of the outlier gave similar results.

Simulant mRNAs are identical to their real counterparts in their 5' and 3' untranslated regions and the encoded protein.

On a single-gene basis, the significance of whether its mRNA is more stable than expected by chance is given by:

R is the number of artificial mRNAs that are more stable than the real transcript, N is the number (1,000) of randomizations (see Box 1 in 128).

The Z-score for stability is given by:

The Z-scores derived from all randomization protocols are normally distributed.

Cellular mRNA levels from normalized microarray data on Affymetrix chips were obtained from SymAtlas 129. We identified the expression profile for each gene by BLASTing mRNA sequences against the probes for the GNF1M chip 130, which has measurements from 61 non-redundant tissue types (the five 'embryo' tissues were ignored). We used the 45-tissue dataset 84 from the U74A chip for six genes where the suggested BLAST hit from GNF1M were not syntenically feasible. For each tissue we took the mean level across replicate hybridizations. Breadth was set to 0 if AD < 50 in all tissues.

To determine whether the incorporation of long genes substantially biased our results, for each modification/randomization protocol, we considered the effect of removing the half of the dataset containing the longest genes. Given that this subset of small mRNAs is by necessity half the size of the full dataset, it is inevitable that P-values will be increased. The issue is whether they have increased more than would be expected had we randomly sampled half the dataset. To this end, we randomly extracted 36 genes and re-calculated the significance from t-tests. This was repeated 10,000 times per modification/randomization protocol, yielding the underlying distribution in P-values that would be expected were sequence length unimportant. The observed P-value (for the shortest genes) was then compared to this expected distribution (see Additional data file 3).